Abstract: We consider active scalar equations ${\partial }_t\theta +\mathrm{\nabla }\cdot (u\theta )=0$, where $u=T[\theta ]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator. We prove that when $T$ is not an odd multiplier, there are nontrivial, compactly supported solutions weak solutions, with Holder regularity $C_{t,x}^{1/9-}$. In fact, every integral conserving scalar field can be approximated in $D^{\prime }$ by such solutions, and these weak solutions may be obtained from arbitrary initial data. We also show that when $T$ is odd, weak limits of solutions are solutions, so that the $h$-principle for odd active scalars may not be expected. This is a joint work with Phillip Isett (MIT).